The primary objective of this proposed project is three-fold. First, we will develop a novel (k, t)-space theoretical framework for imaging of a time-varying objects. Second, we will develop optimal data acquisition and image reconstruction methods for dynamic magnetic resonance imaging. Third, we will carry out necessary simulation and experimental studies to verify the new imaging theory and algorithm. This proposed work is based on our recent breakthroughs in time- sequential sampling theories and constrained imaging. It has the potential to revolutionize the way in which magnetic resonance imaging data are collected and processed from moving objects such as the beating heart. Potential applications of the proposed work include three- dimensional cardiac imaging, functional brain mapping, and interventional imaging. Although the proposed work is focused on magnetic resonance imaging, the results will also be applicable to other imaging modalities, such as x-ray tomography. It is worth noting that although researcher and clinicians are sometimes weary of using a priori constraints in diagnostic imaging, constrained image reconstruction has been successfully used in various imaging applications, including optical imaging, astronomical imaging, x-ray imaging, etc. While we are approaching the physical speed limit with MRI, use of advanced sampling strategies and a priori information appears to be the only way that would provide us the level of speed enhancement to enable 3D real-time imaging.